Try Like This:
Use your All code Inside Update Panels
<asp:UpdatePanel ID="UpdatePanel1" runat="server">
<ContentTemplate>
// All Controls Placed Here
</ContentTemplate><Triggers>
</Triggers> </asp:UpdatePanel>
By default it will use Asynchronous postback Code:
<asp:Label ID="Label1" runat="server" Text="شخص :"></asp:Label></td>
<td>
<asp:DropDownList ID="DropDownList1" EnableViewState="true" AutoPostBack="true" runat="server" OnSelectedIndexChanged="DropDownList1_SelectedIndexChanged">
<asp:ListItem Selected="True">حقیقی</asp:ListItem>
<asp:ListItem>حقوقی</asp:ListItem>
</asp:DropDownList>
</td>
</tr>
<asp:Panel ID="pnlname" runat="server">
<tr>
<td>
<asp:Label ID="Label2" runat="server" Text="نام و نام خانوادگی : "></asp:Label>
</td>
<td>
<asp:TextBox ID="txtname" runat="server" Width="415px"></asp:TextBox>
</td>
</tr></asp:Panel>
<asp:Panel ID="pnlMname" runat="server">
<tr>
<td>
<asp:Label ID="Label3" runat="server" Text="نام و نام خانوادگی مسئول : "></asp:Label>
</td>
<td>
<asp:TextBox ID="txtmname" Width="415px" runat="server"></asp:TextBox>
</td>
</tr></asp:Panel>
<tr>
<td>
<asp:Label ID="Label4" runat="server" Text="شماره قرارداد : "></asp:Label>
</td>
<td>
<asp:TextBox ID="txtIdgharardad" Width="415px" runat="server"></asp:TextBox>
</td>
</tr>
<tr>
<td>
<asp:Label ID="Label7" runat="server" Text="علت درخواست اعزام کارشناس : "></asp:Label>
</td>
<td>
<asp:TextBox ID="txtellat" Width="415px" runat="server" Height="194px" TextMode="MultiLine"></asp:TextBox>
</td>
</tr>
<tr>
<td>
<asp:Label ID="Label5" runat="server" Text="شماره همراه : "></asp:Label>
</td>
<td>
<asp:TextBox ID="txtNumber" Width="415px" runat="server"></asp:TextBox>
</td>
</tr>
<tr>
<td>
<asp:Label ID="Label6" runat="server" Text="شماره ثابت : "></asp:Label>
</td>
<td>
<asp:TextBox ID="txtSnumber" Width="415px" runat="server"></asp:TextBox>
</td>
</tr>
<tr>
<td>
<asp:Button ID="Button1" runat="server" OnClick="Button1_Click" Text="ثبت درخواست" />
</td>
<td>
</td>
</tr>
</table>
</ContentTemplate><Triggers>
</Triggers> </asp:UpdatePanel>